US11035754B2 - Single-ended probing through a multimode fiber having distributed reflectors - Google Patents
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- G01D5/353—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre
- G01D5/35306—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre using an interferometer arrangement
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- G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
- G01M11/30—Testing of optical devices, constituted by fibre optics or optical waveguides
- G01M11/31—Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter and a light receiver being disposed at the same side of a fibre or waveguide end-face, e.g. reflectometers
- G01M11/3172—Reflectometers detecting the back-scattered light in the frequency-domain, e.g. OFDR, FMCW, heterodyne detection
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Definitions
- Various example embodiments relate to fiber optics and, more specifically but not exclusively, to optical imaging and sensing using multimode fibers.
- OCT optical coherence tomography
- FIG. 1 shows a block diagram of an optical system according to an embodiment
- FIG. 2 shows a schematic view of a multimode fiber that can be used in the optical system of FIG. 1 according to an embodiment
- FIG. 4 shows a flowchart of a data-acquisition method that can be used to operate the optical system of FIG. 1 according to an embodiment
- FIG. 5 shows a flowchart of a signal-processing method that can be used in the optical system of FIG. 1 according to an embodiment.
- a multimode optical fiber When an object is imaged through a multimode fiber, light from the object being imaged typically propagates through the fiber on different modes thereof. Due to modal dispersion and mode mixing, such a multimode optical fiber may cause the image produced by the light received from the end of the fiber to appear blurred.
- image-processing techniques are capable of significantly improving the quality of (e.g., removing the blur from) images obtained by light transmitted through a multimode optical fiber.
- image-processing techniques typically require the knowledge of the transfer matrix H of the fiber through which the image is acquired.
- FIG. 1 shows a block diagram of an optical system 100 according to an embodiment.
- system 100 may be adapted for remote optical characterization or remote optical communication applications, e.g., for fiber-optic component and module characterization, distributed optical sensing, biomedical imaging, OCT, or other applications.
- system 100 may be a subsystem of the larger system designed for one of these specific applications.
- System 100 comprises a tunable light source (TLS) 104 , interferometers 110 and 120 , and an optical receiver 150 .
- Electrical output signals 158 1 and 158 2 generated by receiver 150 are converted into a digital form using an analog-to-digital converter (ADC) 160 , and the resulting digital samples 162 are processed by a digital signal processor (DSP) 170 .
- a memory 180 operatively coupled to DSP 170 is configured to store the data representing the various digital signals received and/or generated by DSP 170 , e.g., the sequentially temporally received signal samples.
- An electronic controller 190 can be used to control and/or communicate with the various components of system 100 , e.g., as further described below.
- fiber 140 is shown in FIG. 1 as being inserted through an opening 142 into a cavity 144 .
- a distal end 146 of fiber 140 is placed in proximity to an object 148 located inside cavity 144 such that at least some parts of said object can be optically probed (e.g., illuminated and reflectively imaged to form 2-dimensional or 3-dimensional pixelated images of said parts) through the fiber.
- fiber 140 may be bent into a substantially arbitrary shape, e.g., as indicated in FIG. 1 .
- the delimiters (e.g., walls) of cavity 144 and the relatively small size of opening 142 encumber access to distal end 146 in a manner that does not allow the light emitted out from the distal end to be directly detected thereat.
- TLS 104 may be a pulsed or continuous-wave light source and may be an about continuously wavelength-tunable, external-cavity laser diode operating in the C and/or L communication bands.
- An example tuning range may be, e.g., from about 2 nm to about 40 nm and be spectrally located near 1550 nm.
- the tuning rate may be, e.g., between 20 and 80 nm/s.
- the wavelength (frequency) sweep of TLS 104 can be controlled, e.g., by way of a control signal 192 applied to the TLS by controller 190 .
- An asymmetric optical coupler 108 may be coupled to the output of TLS 104 and may be operated to split the light beam generated by the TLS into two portions.
- the first portion is applied to interferometer 110 .
- the second portion is applied to interferometer 120 .
- the intensity ratio between the first and second portions can be, e.g., 10:90 or 5:95.
- Interferometer 110 comprises interferometer arms 114 1 and 114 2 connected between optical couplers 112 and 116 .
- optical couplers 112 and 116 can be 3-dB couplers.
- the non-zero differential delay of interferometer arms 114 1 and 114 2 is selected such that an optical interference signal 118 generated at the output of optical coupler 116 has a desired (e.g., radio) beat frequency as the wavelength of TLS 104 is temporally swept.
- a photodetector (e.g., a photodiode) 156 3 operates to convert optical interference signal 118 into a corresponding electrical signal 158 3 having the beat frequency.
- Signal 158 3 is then used, as known in the pertinent art, to trigger data acquisition at the outputs of receiver 150 .
- MS MUX 132 operates to spatially shape (e.g., phase and/or intensity filter), and e.g., to optionally polarization shape, the optical signals applied to the M input ports 131 1 - 131 M thereof to cause each of the resulting spatially shaped signals to have, e.g., a transverse electric-field distribution that will substantially match the electric-field distribution of the corresponding guided (e.g., LP) mode when received at the proximate end-face of fiber 140 .
- MS MUX 132 then combines the spatially shaped signals and applies the resulting combined optical signal to port A of circulator 134 .
- the number M can be a different respective positive integer, e.g., 1, 2, 3, and so on.
- MS MUX 132 only one input port, i.e., input port 131 1 , of MS MUX 132 is connected to receive light from TLS 104 .
- MS MUX 132 operates as a transverse spatial mode-selective filter that can be configured and reconfigured to selectively excite one transverse-spatial propagation mode of the multimode optical fiber 140 at a time.
- two or more input ports 131 m of MS MUX 132 may be connected to receive light from TLS 104 , e.g., as described in more detail below.
- MS DMUX 136 can be (re)configured in response to a control signal 196 generated by controller 190 , e.g., to select output light from different respective ones of the transverse spatial propagation modes of the multimode optical fiber 140 to the different output ports 131 .
- the selected mode(s) can be changed for each port, if appropriate or necessary for the intended function or mode of operation of system 100 .
- MS MUX 132 and MS DMUX 136 can be implemented using two respective instances (e.g., nominal copies) of the same physical device connected to transmit light signals in opposite directions, i.e., by inverting optical inputs with optical outputs.
- MS MUX 132 and MS DMUX 136 can be implemented using at least some mode-selective devices that are commercially available, e.g., from CAILabs, Phoenix Photonics, and/or Kylia, as evidenced by the corresponding product-specification sheets, which are also incorporated herein by reference in their entirety.
- ADC 160 digitizes electrical signals 158 1 and 158 2 , when triggered by signal 158 3 , to generate digital samples 162 for further processing in DSP 170 .
- a control signal 198 supplied by controller 190 enables DSP 170 to sort and/or annotate different sets of digital samples 162 to specify the respective pertinent configuration parameters corresponding to each set.
- pertinent configuration parameters may include annotations of corresponding excitation and reception transverse-spatial propagation modes for the light to and from the multimode optical fiber 140 with or without designation(s) of polarization modes.
- Further modifications may include: (i) inserting an additional 1 ⁇ M optical coupler, e.g., an optical power splitter or an optical wavelength demultiplexer, into interferometer arm 124 1 ; (ii) adding (M ⁇ 1) sets of optical couplers 126 and receivers 150 such that each of output ports 137 1 - 137 M can have a respective circuit analogous to that shown in FIG. 1 coupled thereto; and (iii) connecting the added receivers to DSP 170 , e.g., using one or more additional ADCs.
- this second modification with the optical DEMUX may cause each output port 137 1 - 137 M to output light of a different wavelength.
- said alternative embodiment enables multiple combinations of input/output modes of fiber 140 to be probed per wavelength sweep of TLS 104 , e.g., based on the simultaneous use of different probe wavelengths and the modifications introducing optical DEMUXes as already described.
- the embodiment shown in FIG. 1 can be used to probe a single combination of (input mode/output mode) of fiber 140 per wavelength sweep of TLS 104 , e.g., as described in reference to FIG. 4 .
- FIG. 2 shows a schematic view of fiber 140 according to an embodiment.
- fiber 140 has a continuous distributed Bragg reflector (DBR) 210 along the fiber length.
- DBR distributed Bragg reflector
- a first (proximal) end 202 of this fiber 140 is configured to be connected to port B of circulator 134 , e.g., using a suitable adapter or connector (not explicitly shown in FIG. 2 ).
- distal end 146 of fiber 140 is suitable for insertion into cavity 144 (also see FIG. 1 ).
- the transmission/reflection characteristics of DBR 210 can be selected such that: (i) a first relatively large portion of the input light applied to end 202 can reach end 146 ; and (ii) a second relatively large portion of the input light applied to end 202 is reflected by DBR 210 and returned back to end 202 .
- the first portion can be such as to enable imaging of object 148 through fiber 140 .
- the second portion can be such as to enable measurements of the transfer matrix H, e.g., as described further below.
- the second relatively large portion may be, e.g., small enough so that multiple reflections of the same light along the length of the multimode optical fiber 140 can be substantially neglected when determining a particular element of the optical transfer or channel matrix of the multimode optical fiber 140 from measurement(s) of light reflected therein.
- FIG. 3 shows a schematic view of fiber 140 according to an alternative embodiment.
- fiber 140 has a plurality of distinct DBRs 310 1 - 310 K along the fiber length.
- the distance between adjacent DBRs 310 can be several millimeters.
- a first (proximal) end 302 of this fiber 140 is connectable to port B of circulator 134 .
- distal end 146 of fiber 140 can be inserted into cavity 144 .
- the plurality of DBRs 310 1 - 310 K may have a small enough combined reflectivity, e.g., such that reflection of the same light by multiple DBRs 310 1 - 310 K can be substantially neglected when determining the optical transfer or channel matrix for a short segment of the fiber 140 from measurement(s) of reflected light.
- the transmission/reflection characteristics of DBRs 310 1 - 310 K can be selected such that: (i) a first relatively large portion of the input light applied to end 302 can reach end 146 ; and (ii) a second relatively large portion of the input light applied to end 302 is reflected by DBRs 310 1 - 310 K and returned back to end 302 .
- different DBRs 310 k may be nominally identical. In some other embodiments, different DBRs 310 k may differ from each other in one or more characteristics, such as reflectivity, spatial period, and/or separation from the adjacent DBRs 310 k ⁇ 1 and 310 k+1 .
- FIG. 4 shows a flowchart of a data-acquisition method 400 that can be used to operate system 100 according to an embodiment. Method 400 is described in continuing reference to FIG. 1 .
- Method 400 begins at step 402 , in which the number N corresponding to the currently connected fiber 140 is specified to controller 190 , where N is the number of transverse-spatial and/or polarization propagation modes supported by the fiber.
- N is the number of transverse-spatial and/or polarization propagation modes supported by the fiber.
- V 2 ⁇ ⁇ ⁇ ⁇ a ⁇ ⁇ NA ( 1 )
- NA the numerical aperture
- the guided modes of the fiber can generally be classified as (i) transverse electric (TE) modes, for which the axial component of the electric field is zero; (ii) transverse magnetic (TM) modes, for which the axial component of the magnetic field is zero; and (iii) HE or EH modes, for which neither the axial component of the electric field nor the axial component of the magnetic field is zero.
- TE transverse electric
- TM transverse magnetic
- HE or EH modes for which neither the axial component of the electric field nor the axial component of the magnetic field is zero.
- controller 190 generates control signal 192 to cause TLS 104 to perform a wavelength sweep.
- the resulting electrical signal 158 3 triggers ADC 160 to digitize the corresponding electrical signals 158 1 and 158 2 , thereby generating the corresponding (i, j)-th digital samples 162 .
- said digital samples 162 may need to be processed by DSP to derive therefrom the corresponding set S ij .
- the set S ij represents a complex-valued time-dependent waveform W ij (t), with the different digital samples of the set S ij being the samples of the waveform W ij (t) corresponding to different respective times t.
- the set S ij is then saved in memory 180 , e.g., for further processing using method 500 (see FIG. 5 ).
- the index j may be changed by one.
- Step 414 serves to verify that the incremented value of the index j is still within the valid range, which is defined as 1 ⁇ j ⁇ N. If the index j is within the valid range, then the processing of method 400 is directed back to step 408 . Otherwise, the processing of method 400 is directed to step 416 .
- the index i may be changed by one.
- Step 418 serves to verify that the incremented value of the index i is still within the valid range, which is defined as 1 ⁇ i ⁇ N. If the index i is within the valid range, then the processing of method 400 is directed back to step 406 . Otherwise, the processing of method 400 is terminated.
- the sets S ij may be, e.g., optionally processed to perform corrections that take into account possible deviations (if any) due to a linear wavelength sweep, i.e., of TLS 104 , from a linear function expressed by Eq. (4):
- each of digital spectra W′ ij ( ⁇ ) generated at step 502 is Fourier-transformed. Prior to the Fourier transform, the argument k may need to be converted into the beat frequency f.
- the result of the processing performed at step 504 is the plurality of digital time-domain responses A ij ( ⁇ ), where ⁇ is the time of flight of the corresponding portion of the probe light through fiber 140 .
- each of time-domain responses A ij ( ⁇ ) is converted into the corresponding response function A ij (x), where x is the distance from the proximal end (e.g., 202 , FIG. 2 , or 302 , FIG. 3 ) along the span of fiber 140 .
- This conversion can be performed, e.g., using the known linear relationship between the time of flight ⁇ and the distance x.
- the processing performed at step 506 thereby generates N 2 response functions A ij (x).
- Each of the response functions A ij (x) is a discrete function in which the argument x, i.e., x is the reflection distance or location in the multimode optical fiber 140 , can have one of the values x 1 ⁇ x 2 ⁇ . . . ⁇ x Q , where Q is the number of digital samples in the response function A ij (x).
- the matrix elements of each response matrix A q are expressed by Eq. (5) as follows:
- a ij (q) A ij ( x q ) (5)
- the response function A ij (x) is, e.g., the (i, j)-th element of a roundtrip transfer matrix that includes a back reflection in the multimode optical fiber 140 at the point x, i.e., for light transmitted into fiber mode “j” and then, received from fiber mode “i”.
- Such a response function does not always determine the single-direction, transfer matrix H of the multimode optical fiber 140 , because roundtrip propagation may introduce, e.g., phase ambiguities in the relationship between single-direction and roundtrip transfer matrices.
- Steps 510 - 520 of method 500 implement a recursive algorithm, using which the fiber transfer matrix H is estimated from the response matrices A q of step 508 , e.g., in a manner that removes phase ambiguities.
- the algorithm is based on an approximation according to which, for any spatially resolved pair of coordinates (x q , x q+1 ), i.e., which are locations of the left and right ends of a corresponding segment of the optical fiber 140 whose length is
- differences between the phase changes of the different fiber modes in each successive pair of such segments are, e.g., smaller than ⁇ . That is, each fiber segment for a successive pair of coordinates, in the set ⁇ x 1 , . . . , x Q ⁇ , is short enough to not cause phase ambiguities in determinations of the elements of the single-direction transfer matrices therefrom.
- Step 512 serves to verify that the index (q+1) is within the valid range, which is defined as 1 ⁇ q ⁇ Q. If the index (q+1) is within the valid range, then the processing of method 500 is directed to step 514 . Otherwise, the processing of method 500 is directed to step 520 .
- the matrices P L and P R are computed, e.g., in DSP 170 , as follows.
- the matrix H k is the transfer matrix of the k-th successive fiber segment; and the superscript T denotes the transposed matrix.
- Method 500 may include performing one or more iterations of at least some steps or sequences of steps shown in FIG. 5 to ensure that the final single-direction transfer matrix H has been properly computed, i.e., to remove the risk of any phase ambiguities.
- method 500 involves initially selecting a set of Q successive points ⁇ x 1 , x 2 , . . . , x Q ⁇ , i.e., x 1 ⁇ x 2 ⁇ . . . ⁇ x Q along the multimode optical fiber 140 , at which corresponding values of the matrix A ij (x q ) are used to subsequently iteratively, multiplicatively determine the value of H.
- method 500 may be repeating some of the steps for a new larger set of 2Q successive points ⁇ x 1 , x 2 , . . . , x 2Q ⁇ along the fiber, wherein the distance between the successive ones of the points is smaller than the distance between the successive ones of the original Q points, e.g., successive separations may be 1 ⁇ 2 of the original ones in the new set of 2Q points. If the new set of 2Q successive points along the multimode optical fiber 140 leads to a determination of the single-direction transfer matrix H with elements having about the same values, i.e., below threshold differences in amplitudes and phases of the re-determined matrix elements, method 500 is terminated.
- method 500 may be repeated by again doubling the total number of points along the optical fiber 140 , which are used for values of the matrix A ij (x q ) and for the iterative and multiplicative determination of the single-direction transfer H as explained in reference to equations (6)-(9), i.e., for yet shorter segments of the multimode optical fiber 140 .
- an apparatus comprising: a tunable laser (e.g., 104 , FIG. 1 ) configured to generate probe light and controllable to sweep a wavelength of said probe light; a first configurable optical filter (e.g., 132 , FIG. 1 ) to transmit a received part of said probe light primarily to a selectable spatial propagation mode of the multimode optical fiber at a first end thereof; a second configurable optical filter (e.g., 136 , FIG.
- a tunable laser e.g., 104 , FIG. 1
- a first configurable optical filter e.g., 132 , FIG. 1
- a second configurable optical filter e.g., 136 , FIG.
- an optical interferometer e.g., 120 , FIG. 1
- a digital signal processor e.g., 170 , FIG. 1
- the apparatus further comprises the multimode optical fiber (e.g., 140 , FIGS. 1-3 ), the multimode optical fiber having reflectors distributed along at least a portion thereof (e.g., 210 , FIG. 2 ; 310 , FIG. 3 ).
- the multimode optical fiber e.g., 140 , FIGS. 1-3
- the multimode optical fiber having reflectors distributed along at least a portion thereof (e.g., 210 , FIG. 2 ; 310 , FIG. 3 ).
- the multimode optical fiber has spatially separated gratings (e.g., 310 , FIG. 3 ) distributed over at least half of the length of the multimode optical fiber.
- the apparatus is capable of performing optical coherence tomography imaging with light received from the multimode optical fiber.
- the apparatus further comprises an electronic controller (e.g., 190 , FIG. 1 ) capable of causing the first and second configurable optical filters to change at least one of the selectable spatial propagation mode and the chosen spatial propagation mode.
- an electronic controller e.g., 190 , FIG. 1
- the apparatus is configured to measure said optical interference signal in a manner that is sensitive to polarization state of the light of the chosen spatial propagation mode.
- the digital signal processor is configured to estimate the single-direction transfer matrix of the multimode optical fiber using estimates of transfer matrices of different segments of the multimode optical fiber.
- the digital signal processor is further configured to estimate roundtrip transfer matrices for the different segments of the multimode optical fiber, each of the roundtrip transfer matrices being a transfer matrix for light reflected at a corresponding end region of a respective fiber segment.
- the apparatus further comprises a mode-selective demultiplexer (e.g., 136 , FIG. 1 ) that includes the second configurable optical filter.
- a mode-selective demultiplexer e.g., 136 , FIG. 1
- an apparatus comprising: an optical frequency-domain reflectometer having a tunable light source (e.g., 104 , FIG. 1 ), an optical interferometer (e.g., 120 , FIG. 1 ), and an optical receiver (e.g., 150 , FIG. 1 ), the optical interferometer including a multimode optical fiber (e.g., 140 , FIGS. 1-3 ) having reflectors (e.g., 210 , FIG. 2 ; 310 , FIG.
- a multimode optical fiber e.g. 140 , FIGS. 1-3
- reflectors e.g., 210 , FIG. 2 ; 310 , FIG.
- the digital signal processor is configured to estimate the single-direction fiber transfer matrix using estimates of transfer matrices of segments of the multimode optical fiber of different lengths.
- the reflectors include a plurality of spatially separated Bragg gratings (e.g., 310 k , FIG. 3 ), the Bragg gratings being distributed over at least half of the length of the multimode optical fiber.
- the reflectors include a Bragg grating (e.g., 210 , FIG. 2 ) extending along at least half of the length of the multimode optical fiber.
- the apparatus further comprises an optical endoscope including the multimode optical fiber; and wherein the apparatus is capable of producing optical images with light received from the multimode optical fiber.
- the apparatus is configured to perform optical coherence tomography imaging with light received via the multimode optical fiber.
- an apparatus comprising: a tunable laser (e.g., 104 , FIG. 1 ) configured to generate probe light whose wavelength is swept from a first wavelength to a second wavelength (e.g., ⁇ 1 and ⁇ 2 respectively, Eq. (4)); an interferometer (e.g., 120 , FIG. 1 ) connected to receive the probe light from the tunable laser and apply output light to an optical receiver (e.g., 150 , FIG.
- a tunable laser e.g., 104 , FIG. 1
- a second wavelength e.g., ⁇ 1 and ⁇ 2 respectively, Eq. (4)
- an interferometer e.g., 120 , FIG. 1
- an optical receiver e.g., 150 , FIG.
- the output light being generated using optical interference between respective portions of the probe light after said respective portions pass through a reference arm (e.g., 124 1 , FIG. 1 ) and a measurement arm (e.g., 124 2 , FIG. 1 ) of the interferometer, respectively; and a multimode optical fiber (e.g., 140 , FIGS. 1-3 ) having distributed reflectors (e.g., 210 , FIG. 2 ; 310 , FIG. 3 ) therein, a proximal end of the multimode optical fiber being connected to the measurement arm; wherein the interferometer comprises: a first configurable mode-selective filter (e.g., 132 , FIG.
- a second configurable mode-selective filter (e.g., 136 , FIG. 1 ) connected to select a guided mode of the multimode optical fiber for generating the output light by filtering a portion of the probe light reflected by the distributed reflectors and received by the measurement arm through the proximal end.
- the optical receiver is polarization-sensitive.
- the reference arm includes a polarization controller (e.g., 125 , FIG. 1 ).
- the digital signal processor is configured to estimate the fiber transfer matrix using estimates of segment transfer matrices (e.g., H k , Eqs. (6)-(9); computed at 516 , FIG. 5 ) corresponding to individual segments of the multimode optical fiber located between different ones of the distributed reflectors.
- segment transfer matrices e.g., H k , Eqs. (6)-(9); computed at 516 , FIG. 5
- the apparatus further comprises a mode-selective demultiplexer (e.g., 136 , FIG. 1 ) that includes the second configurable mode-selective filter.
- a mode-selective demultiplexer e.g., 136 , FIG. 1
- the interferometer being configured to generate output light (e.g., 128 , FIG. 1 ) in response to probe light received from the tunable light source, the output light being sensitive to guided modes of the multimode optical fiber controllably selected in the interferometer; and a digital signal processor (e.g., 170 , FIG. 1 ) configured to estimate a fiber transfer matrix (e.g., H, at 520 , FIG. 5 ) in response to measurements of the output light performed by the optical receiver.
- output light e.g., 128 , FIG. 1
- a digital signal processor e.g., 170 , FIG. 1
- a fiber transfer matrix e.g., H, at 520 , FIG. 5
- the digital signal processor is configured to estimate the fiber transfer matrix using estimates of segment transfer matrices (e.g., H k , Eqs. (6)-(9); computed at 516 , FIG. 5 ) corresponding to individual segments of the multimode optical fiber located between different ones of the distributed reflectors.
- segment transfer matrices e.g., H k , Eqs. (6)-(9); computed at 516 , FIG. 5
- the distributed reflectors include a plurality of distinct distributed Bragg gratings (e.g., 310 k , FIG. 3 ).
- figure numbers and/or figure reference labels in the claims is intended to identify one or more possible embodiments of the claimed subject matter in order to facilitate the interpretation of the claims. Such use is not to be construed as necessarily limiting the scope of those claims to the embodiments shown in the corresponding figures.
- the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. The same type of distinction applies to the use of terms “attached” and “directly attached,” as applied to a description of a physical structure. For example, a relatively thin layer of adhesive or other suitable binder can be used to implement such “direct attachment” of the two corresponding components in such physical structure.
- program storage devices e.g., digital data storage media, which are machine or computer readable and encode machine-executable or computer-executable programs of instructions where said instructions perform some or all of the steps of methods described herein.
- the program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks or tapes, hard drives, or optically readable digital data storage media.
- the embodiments are also intended to cover computers programmed to perform said steps of methods described herein.
- processors may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software.
- the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared.
- processor or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage.
- DSP digital signal processor
- ASIC application specific integrated circuit
- FPGA field programmable gate array
- ROM read only memory
- RAM random access memory
- non volatile storage Other hardware, conventional and/or custom, may also be included.
- any switches shown in the figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.
- circuitry may refer to one or more or all of the following: (a) hardware-only circuit implementations (such as implementations in only analog and/or digital circuitry); (b) combinations of hardware circuits and software, such as (as applicable): (i) a combination of analog and/or digital hardware circuit(s) with software/firmware and (ii) any portions of hardware processor(s) with software (including digital signal processor(s)), software, and memory(ies) that work together to cause an apparatus, such as a mobile phone or server, to perform various functions); and (c) hardware circuit(s) and or processor(s), such as a microprocessor(s) or a portion of a microprocessor(s), that requires software (e.g., firmware) for operation, but the software may not be present when it is not needed for operation.”
- This definition of circuitry applies to all uses of this term in this application, including in any claims.
- circuitry also covers an implementation of merely a hardware circuit or processor (or multiple processors) or portion of a hardware circuit or processor and its (or their) accompanying software and/or firmware.
- circuitry also covers, for example and if applicable to the particular claim element, a baseband integrated circuit or processor integrated circuit for a mobile device or a similar integrated circuit in server, a cellular network device, or other computing or network device.
- any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the disclosure.
- any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.
- the term “provide” with respect to a system, device, or component encompasses designing or fabricating the system, device, or component; causing the system, device, or component to be designed or fabricated; and/or obtaining the system, device, or component by purchase, lease, rental, or other contractual arrangement.
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Abstract
Description
where a is the fiber-core radius, and NA is the numerical aperture. For a step-index fiber, the numerical aperture is given by Eq. (2):
NA=√{square root over (n 1 2 −n 2 2)} (2)
where n1 is the refractive index of the fiber core, and n2 is the refractive index of the fiber cladding.
In the approximation of weak guidance for generally cylindrical fibers, the TE, TM, HE, and EH guided modes approximately become the modes that are conventionally referred to as the linearly polarized (LP) modes. Representative intensity and electric-field distributions of several low-order LP modes are graphically shown, e.g., in U.S. Pat. No. 8,705,913, which is incorporated herein by reference in its entirety.
where λ1 and λ2 are the start and end wavelengths of the sweep, respectively; and ts is the duration of the wavelength sweep. The result of the processing performed at
A ij (q) =A ij(x q) (5)
The response function Aij(x) is, e.g., the (i, j)-th element of a roundtrip transfer matrix that includes a back reflection in the multimode
P L ×H q+1 T ×H q+1 ×P R =A q+1 (8)
The computed transfer matrix H is then saved in
Claims (13)
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